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100cubic centimetres of seawater of density 1150kilograms per cubic meters is mixed with 100cubic centimetres of fresh water of density 1000kilograms per cubic meters. determine density of the mixture​



Answer :

Answer:

The density of the mixture = 1075 kg/m³.

Explanation:

We can find the density of the mixture using this formula:

[tex]\boxed{\rho=\frac{m}{V} }[/tex]

where:

  • [tex]\rho[/tex] = density
  • [tex]m[/tex] = mass
  • [tex]V[/tex] = volume

Given:

  • [tex]V_1[/tex] = 100 cm³ = 0.0001 m³
  • [tex]\rho_1[/tex] = 1150 kg/m³
  • [tex]V_2[/tex] = 100 cm³ = 0.0001 m³
  • [tex]\rho_2[/tex] = 1000 kg/m³

[tex]\displaystyle \rho_1=\frac{m_1}{V_1}[/tex]

[tex]\displaystyle 1150=\frac{m_1}{0.0001}[/tex]

[tex]m_1=0.115\ kg[/tex]

[tex]\displaystyle \rho_2=\frac{m_2}{V_2}[/tex]

[tex]\displaystyle 1000=\frac{m_1}{0.0001}[/tex]

[tex]m_1=0.1\ kg[/tex]

[tex]total\ volume\ of\ mixture\ (V_3)=V_1+V_2[/tex]

                                           [tex]V_3=0.0001+0.0001[/tex]

                                           [tex]V_3=0.0002\ m^3[/tex]

[tex]total\ mass\ of\ mixture\ (m_3)=m_1+m_2[/tex]

                                       [tex]m_3=0.115+0.1[/tex]

                                       [tex]m_3=0.215\ m^3[/tex]

[tex]\displaystyle \rho_3=\frac{m_3}{V_3}[/tex]

    [tex]\displaystyle=\frac{0.215}{0.0002}[/tex]

    [tex]\displaystyle=\bf1075\ kg/m^3[/tex]

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